How to Update @@SERVERNAME to Actual Machine Name?
If, for whatever reason, the Windows Computer Name is changed after SQL Server is already installed, then @@SERVERNAME and the information in sys.servers would not automatically reflect the change (sysservers in older SQL versions).
This means that @@SERVERNAME contains the incorrect value for the machine name.
Sometimes, and especially in production environments, the value in that global variable is important and is used as part of business processes.
And if @@SERVERNAME doesn’t reflect the actual server name, it could cause problems.
Alternatively, it’s possible (and maybe even best) to use the SERVERPROPERTY function instead to get the actual server name, or machine name, or instance name. The information available through this function should be up-to-date even after you rename the Windows Computer Name.